论文标题
诱导同质形态和Atsuji超空间
Induced Homeomorphism and Atsuji Hyperspaces
论文作者
论文摘要
鉴于均匀同构度量公式空间$ x $和$ y $，因此证明了Hyperspaces $ c（x）$和$ c（y）$是同型同构的，其中$ c（x）$表示所有非空的封闭子集的收集$ x $，并且与hausdorff距离一样。杰拉尔德·啤酒（Gerald Beer）证明，当$ x $是紧凑或均匀离散时，超空间$ c（x）$是atsuji。 Atsuji空间是紧凑的度量空间以及统一离散空间的概括。在本文中，我们调查了$ x $是atsuji时的空间$ c（x）$，并且获得了一类$ c（x）$的Atsuji子空间。使用获得的结果，获得了Atsuji空间上连续地图的一些固定点结果。
Given uniformly homeomorphic metric spaces $X$ and $Y$, it is proved that the hyperspaces $C(X)$ and $C(Y)$ are uniformly homeomorphic, where $C(X)$ denotes the collection of all nonempty closed subsets of $X$, and is endowed with Hausdorff distance. Gerald Beer has proved that the hyperspace $C(X)$ is Atsuji when $X$ is either compact or uniformly discrete. An Atsuji space is a generalization of compact metric spaces as well as of uniformly discrete spaces. In this article, we investigate the space $C(X)$ when $X$ is Atsuji, and a class of Atsuji subspaces of $C(X)$ is obtained. Using the obtained results, some fixed point results for continuous maps on Atsuji spaces are obtained.
